Formula for the Lateral Area of Solids
The lateral area formula is different for different solid shapes. In the lateral area formula, the base area of the object as well as that of the face parallel to the base are not included.
The lateral area is also referred to as the lateral surface area (LSA) and is always measured in square units.
Formula for the Lateral Area of Cuboids and Cubes
For a cuboid: Lateral Area = 2 (length + breadth) × height.
For a cube: Lateral Area = 4 × (side)\(^2\) .
Formula for the Lateral Area of a Cylinder
Lateral area = 2 × π × r × h = 2πrh, where ‘r’ is the base radius and ‘h’ is the height of the cylinder.
Formula for the Lateral Area of a Cone
Lateral Area = = πrl
where ‘r’ is base radius and ‘l’ is slant height of the cone.
Formula for the Lateral Area of a Sphere
For a sphere the lateral surface area is its curved surface area.
Lateral Area = 4πr\(^2\)
where ‘r’ is the radius of the sphere.
Formula for the Lateral Area of a Hemisphere
For a hemisphere the lateral surface area is its curved surface area.
Lateral Area = 2πr\(^2\)
where ‘r’ is the radius of the hemisphere.
Rapid Recall
Solved Examples
Example 1: Calculate the lateral surface area of a cuboid with dimensions of 8 units, 4 units, and 12 units respectively.
Solution:
As stated in the question,
Length of the cuboid = 8 units
Breadth of the cuboid = 4 units
Height of the cuboid = 12 units
According to the formula,
Lateral area of cuboid = 2 (length + breadth) × height
Substituting the values in the formula,
Lateral area = 2 (8 + 4) x 12
= 2 (12) x 12
= 24 x 12
= 288
Hence, the lateral area of the cuboid is 288 square units.
Example 2: Anthony bought a spherical ball of radius 16 cm. Find its lateral area. Can you find the lateral area of the spherical ball if it is divided into two equal parts?
Solution:
The details already provided,
Radius of the spherical ball = 16 cm
According to the lateral area formula,
Lateral area of sphere = 4πr\(^2\)
Substituting the value of ‘r’ and 3.14 for π in the formula,
Lateral area = 4 x 3.14 x (16)\(^2\)
= 3215.36
Hence, the lateral area of the spherical ball is 3215.36 square centimeters.
Now, if the spherical ball is divided into two equal parts, then we need to find the lateral area for the hemisphere.
As we know, the lateral area formula for a hemisphere is given by, Lateral area of hemisphere = 2πr\(^2\)
Substituting the values in the formula,
Lateral area = 2 x 3.14 x (16)\(^2\)
= 1607.68 cm
Hence, the lateral area for the sphere is 3215.36 cm² and the lateral surface area of a hemisphere is 1607.68 cm² respectively.
Example 3: Find the lateral area of a cylinder with radius 8 units and height 14 units. Take π = \(\frac{22}{7}\).
Solution:
As provided,
Radius of the cylinder = 8 units
Height of the cylinder = 14 units
According to the lateral area formula of a cylinder,
Lateral area = 2πrh
Substituting the values in the formula,
Lateral area = 2 x \(\frac{22}{7}\) x 8 x 14
= 2 x 22 x 8 x 2 [Simplify]
= 704 [Simplify further]
Therefore the lateral area of the given cylinder is 704 square units.
The lateral area formula for a cuboid is given by, 2 (length + breadth) × height.
The lateral area formula for a triangular prism is given by,
Lateral Area = (a + b + c) × h, where (a + b + c) is the perimeter of the base of the prism and h is its height.
Lateral area can be defined as the surface area of the lateral faces of 3D objects. In this case lateral surface area will not include the area of the base and the face parallel to the base.